PORTLAND, Ore. — In 2011, Oregon Governor John Kitzhaber faced a vexing problem: The state had a $2 billion hole in its Medicaid budget and no good way to fill it.

He could cut doctors’ pay by 40 percent, but that might lead to them quitting Medicaid altogether. He could drop patients or benefits, but that would only compound costs in the long run. A former emergency room doctor, Kitzhaber remembers culling the Medicaid rolls in the 1980s, when he served as a state senator.

‘‘When I went back home, and went back to the emergency department, I saw a couple of people who came in who lost coverage under that decision,’’ he said. ‘‘One of them was a guy who had had a massive stroke. These people don’t disappear.’’

So Kitzhaber did something that many before him have done in desperate times. The Democratic governor
who favors cowboy boots rather than dress shoes made a bet that Oregon could not afford to lose.

The deal Kitzhaber struck was this: The Obama administration would give the state $1.9 billion during five years — enough to patch the budget hole.

The catch: To secure that, Oregon’s Medicaid program must grow at a rate that is 2 percent slower than the rest of the country, ultimately generating $11 billion savings during the next decade. If it fails, those federal dollars disappear.

Oregon is pursuing the Holy Grail in health care policy: slower cost growth. If it succeeds, it could set a course for the nation at a pivotal moment for the Affordable Care Act. Under the law, many states will expand Medicaid programs to cover all below 133 percent of the federal poverty line, adding 7 million Americans to the program in 2014 and leaving states looking for the most cost-effective way to cover that influx of patients.

‘This is one where you really have to change how you do business in order to survive.’

In Oregon alone, Medicaid is expected to enroll 400,000 new patients by 2022, nearly doubling its current numbers, according to an Urban Institute analysis.

As Oregon’s population grows, the state has come to realize that Medicaid is not a bottomless bucket of money. The state’s budget cannot sustain that. Instead, it strives to deliver what health policy experts call ‘‘the triple aim’’: higher-quality care that leads to better outcomes, all delivered at a lower cost.

‘‘Oregon is trying to change the way that health care is delivered with incentives to deliver smarter, better care, instead of just imposing budget changes that cut back on health care,’’ said Cindy Mann, director of the Center for Medicaid and State Operations. ‘‘It’s very exciting.’’

Under the new deal, Oregon does not get a lump-sum payment. Instead, the federal government doles out $1.9 billion during five years.

If the state cannot deliver cost savings up front, while hitting certain quality metrics, it is cut off. The money it needs to keep doctor salaries stable and patients’ benefits covered dries up.

‘‘In terms of cost-control experiments, the likes of this are something we have never seen in health care,’’ said John McConnell, a health policy researcher at Oregon Health & Science University who is studying the Oregon Medicaid waiver. ‘‘The natural questions are: Is it going to work? Is the state going to fix the budget? And if they do fix the budget, how are those savings accomplished?’’

As Kitzhaber sees it, failure is not an option. The state’s Medicaid program needs $1.9 billion to make ends meet now, even if it means paying big dividends back to the US government later. It is not unlike a payday loan, with a quick influx of cash and a large obligation to follow.

‘‘There’s no more money,’’ Kitzhaber said. ‘‘This is one where you really have to change how you do business in order to survive.’’

Oregon has a long history of leadership when it comes to the Medicaid program, which covers nearly 62 million low-income and disabled Americans nationwide. In the early 1990s, it was among the first to use a federal waiver to expand limited coverage to all Oregonians living below the poverty line. Oregon’s uninsured rate quickly dropped, from 18 percent in 1994 to 10 percent in 1998.

Maintaining a robust health plan, however, has not been easy. The state’s tax revenue fell during the economic downturn of the early 2000s.

To keep the Medicaid program afloat, the state charged significantly higher co-pays for some: $50 for an emergency room visit and $250 for a trip to the hospital.

Medicaid enrollment shrank by 46 percent as patients affected by the changes left the program — likely relegated to the ranks of the uninsured — between February and December 2003, according to research published in the journal Health Affairs.

Separate research has found that when Medicaid premiums rise by 1 to 5 percent of an uninsured family’s income, their odds of participating drop from 57 to 18 percent.